Back a million years ago, when dinosaurs roamed the earth and I still talked about sports for a living, the New England Patriots parted ways with their coach, Bill Parcells, after the team made a Super Bowl appearance. He was not super-pleased. In fact, he had a parting shot:
“If they want you to cook the dinner, at least they ought to let you shop for some of the groceries.”
I get what he’s saying: if you are holding me accountable for the performance of 53 guys, I should get to pick which guys they are. Well, teachers don’t get to pick. But in the right place, they get to pick how they teach. In one of my first conversations with my new department chair (now a district-level administrator) when I hired on, I found out that our department was moving in the direction of classroom -level autonomy. The state decides what you have to teach, yeah, but you get to decide how to do it.
We do a lot of planning as content teams. Our main focus during this school year is detracking. Instead of offering three ability-grouped sections, there will be “Honors Algebra II”, and just-plain “Algebra II” next year. Those are the options, kid. So we’re spending a lot of time figuring how to support our struggling learners in a faster-paced environment.
Now, they’re not coming around tomorrow to make a movie. Nobody here is doing anything earth-shattering and disruptive, but it is obviously cool to have the freedom to teach in your own style. Occasionally, monumentally cool things happen. Sometimes, it’s a smaller victory. In classic “happy accident” style, I may have stumbled across something cool this week, in terms of the order in which material is presented for maximum learning.
We’re in the midst of a (short) trig unit. Right angle trig, sine and cosine graphs, that’s about it. “Coterminal angles” and “Functions of any angle” gets a drive-by. Law of Sines and Law of Cosines get pushed back to Pre-Cal. There’s probably more emphasis on graphing. But: What if the order flip-flopped? Graph first, then tackle coterminal angles and the general definition of the functions?
Maybe with a Desmos activity?
Yeah, let’s do that.
I feel like I’ve got to lay a pretty good foundation with the graphs. Maybe, emphasize that the graph is periodical and hits the same value multiple times. I think the visual will help my students grasp the concept that there is a sine & cosine value for all of those degree measures, then we can go from there.
My 2nd hour wasn’t having it:
My 5th hour response: marginally better. Then I was out Thursday for an all-day curriculum planning meeting (coincidentally). So we’ll see. If the periodic nature of the sin/cos functions take root, I’ve set the table for Friday beautifully.
We quickly recapped the sin/cos graph assignment Friday at the outset of class, pointing out again how the graph of the function repeats. I’m guardedly optimistic. Let’s roll with Desmos, huh? We started with a card sort of definitions – letting the students do some word root detective work.
They had some mild success at matching words, images, and definitions, and we took a couple of minutes to make sure we were speaking the same language.
(H/T to some of my online PLN friends who helped me tweak this activity. Protip: when smart people give you advice, take it.)
After a couple more screens where we pondered the cyclical nature of the graphs, it’s time to get to the meat and potatoes.
Good news: pretty much everybody could sketch a 135 degree angle. Also good news: most could recall the ratios for sine and cosine. So let’s push the ball upfield. Here’s how to calculate the ratio of any angle. Go.
We ran out of time before we could dive deep into the idea of positive and negative values for the functions.
Ironically, this activity connected much better with my 2nd hour than with my 5th.
But what can I say? Friday afternoon, after lunch, sun shining thru my windows….
At least some of them let their creativity shine thru as well.
So, did this little tweak in the order of sections pay off? Not in a fireworks/shooting stars kind of way. I think the visual of the animated unit circle/sine graph was huge. And I think the Desmos activity was an improvement over me standing there and dishing out notes and giving a written assignment.
The bigger story is the freedom to re-arrange things in such a way that it benefits my students. Writ large, my Alg II planning group met last week to ponder some options for next year, including SBG, but we also took a hard look at the course from a power standards standpoint. We front-loaded the course with Alg II standards, pushed the trig section back to the end of the year, and flip-flopped a couple of units to get balance between 3rd and 4th quarter. Standards-Based Grading has some folks curious, and is being strongly encouraged, but individual teachers have the option whether to implement it.
Sounds to me like as seasoned chefs, a lot of us will be buying our own groceries next year. I feel a little bit like Bobby Flay already.